The symmetric boundary element method for unilateral contact problems

Panzeca, T.; Salerno, Margherita; Terravecchia, S.; Zito, L.

doi:10.1016/j.cma.2007.03.026

Cited by 18 publications

(13 citation statements)

References 20 publications

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“…Some applications of the BEM for Signorini problems can be found in Refs. [2,3,9,11,[14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…Signorini problems come up in the modeling of many realistic science and engineering applications such as the shallow dam problem [1][2][3][4], the electropaint process [3][4][5][6][7], the unilateral contact problem [8,9], the free boundary problem [10,11], and so on. Besides, in the theory of variational inequalities [12,13], a broad class of problems arising in industry, social, economics, finance, pure and applied sciences give rise to Signorini problems.…”

Section: Introductionmentioning

confidence: 99%

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Application of the method of fundamental solutions to 2D and 3D Signorini problems

Zheng

2015

Engineering Analysis with Boundary Elements

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“…Some applications of the BEM for Signorini problems can be found in Refs. [2,3,9,11,[14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Zheng

2015

Engineering Analysis with Boundary Elements

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“…On the basis of the boundary integral method, in its symmetric formulation, the frictionless unilateral contact between two elastic bodies was studied according to the Signorini formulation [14]. A boundary discretization by boundary elements of the two bodies in contact leads to an algebraic formulation in the form of a LCP, discussed by several authors [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…In the previous integral Equations (14), (15) and (16), © p is the plastic strain vector, whose evaluation strategy is defined in the next section.…”

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confidence: 99%

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Active macro‐zone approach for incremental elastoplastic‐contact analysis

Cucco

Terravecchia

Zito

2013

Numerical Meth Engineering

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The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In this paper, we want to treat these complex phenomena together as a linear complementarity problem.A mixed variable multidomain approach is utilized in which the substructures are distinguished into macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted (weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and uses the well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction of the influence matrix (self-stress matrix). The solution of the frictionless contact/detachment problem was performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact or detachment. the integral equations satisfying the boundary and domain conditions, the Signorini equations regarding the contact/detachment conditions rewritten as LCP, and the constitutive relations for rate-independent plasticity.

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Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches

2012

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The object of the paper concerns a consistent formulation\ud of the classical Signorini’s theory regarding the frictionless\ud contact problem between two elastic bodies in the\ud hypothesis of small displacements and strains. The employment\ud of the symmetric Galerkin boundary element method,\ud based on boundary discrete quantities, makes it possible to\ud distinguish two different boundary types, one in contact as\ud the zone of potential detachment, called the real boundary,\ud the other detached as the zone of potential contact, called\ud the virtual boundary. The contact-detachment problem is\ud decomposed into two sub-problems: one is purely elastic,\ud the other regards the contact condition. Following this methodology,\ud the contact problem, dealtwith using the symmetric\ud boundary element method, is characterized by symmetry and\ud in sign definiteness of the matrix coefficients, thus admitting\ud a unique solution. The solution of the frictionless contact-\ud detachment problem can be obtained: (i) through an\ud iterative analysis by a strategy based on a linear complementarity\ud problem by using boundary nodal quantities as check\ud quantities in the zones of potential contact or detachment;\ud (ii) through a quadratic programming problem, based on a\ud boundary min-max principle for elastic solids, expressed in\ud terms of nodal relative displacements of the virtual boundary\ud and nodal forces of the real one

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The symmetric boundary element method for unilateral contact problems

Cited by 18 publications

References 20 publications

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Application of the method of fundamental solutions to 2D and 3D Signorini problems

Active macro‐zone approach for incremental elastoplastic‐contact analysis

Frictionless contact-detachment analysis: iterative linear complementarity and quadratic programming approaches

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